TM Wo„ 377 

 where H is the wave height or twice the wave amplitude, and K is the wave 

 number - 2Tr/L<> With the vertical S axis measured positively upward (at 

 the surface, S^O), then D =fL 



o 



According to simple linear theory, as a wave crosses the transition point 

 from deep to shallow water, the quasi-circular orbits of the wave particles 

 "feel" the bottom boundary The circular orbits are transformed into 

 ellipses, and the eccentricity of the elliptical orbits increases with 

 depth Since at the bottom boundary the vertical component must vanish, 

 the elliptical orbits degenerate at the bottom into horizontal rectilinear 

 oscillations 9 



Two wave attributes are of importance to the design of the instrumentation 

 and to the measuring procedures. For deep and intermediate waves having 

 small amplitudes, the first order approximations for the horizontal and 

 vertical components of particle velocity are given as a function of depth 

 and time (see Coulson, 1958)0 



1^= g <r e * * cos <rt , (II _ 5) 



o^fccre^s/A/cr*. (I]>6) 



1 2. s*Nh K& (n-7) 



2- s7aM KD ^ /A/Cr ^ (H-8) 



U) 



The subscripts d and i refer to deep and intermediate „ These four equations 

 apply for a water level profile that varies as cos<?~-& , In the case of inter- 

 mediate waves s at the bottom, where B = -D, w vanishes 



Particle displacement is defined as the total excursion taken by the 

 particle along either the horizontal or vertical axis,; and is obtained 

 by integration (with respect to time) of the particle velocity components „ 

 The absolute values for particle displacements can be approximated bys 



\ij\ *'.. f & Kt cos <r-k 



\l 



= § e KE s«A/cr^ 



(II-9) 



(11-10) 



IS I = 



* -s^rTW^™ (II . U) 



16 



